Abstract: The contents of the following work carefully analyze the conditions of the relative sliding between involute gear teeth, when they are brought into contact; besides, in accordance with the magnitudes and the law of variations of the relative sliding, a simple graphical method is thus utilized to determine the meshing efficiencies of those gears that have a period of contact ε≤2. An example is given in the paper. The author by means of an analytic method, derives an accurate formula for the calculation of the meshing efficiencies of the involute gears, and the formula is consequently applied in the example to check the result of the graphical work. He finds that the graphical work is accurate enough for the ordinary engineering purposed. Bearing loss due to friction is neglected in this consideration.